The Valuation of Inflation-Indexed and FX Convertible Bonds

Abstract

Issuing convertible bonds has become a popular way of raising capital by corporations in the last few years. An important subgroup is convertibles linked to a price index or exchange rate. In this paper we extend the convertible pricing models of Tsiveriotis and Fernandes (1998) and McConnell and Schwartz (1986) to the case of indexation of the promised payments of the convertible to a general price index or to the price of foreign exchange. The theoretical framework derived in this paper considers two sources of uncertainty: both the underlying stock price and the consumer-price-index (or equivalently foreign-currency) are stochastic, and incorporate credit risk in the analysis. The extensions of two models enable to establish upper and lower bounds for the price of the indexed convertible. We approximate the pricing equations by using Rubinstein (1994) three-dimensional binomial tree, and we describe the numerical solution. We investigate and compare the models with respect to the characteristics of the issuer and the economic environment. Moreover, we demonstrate the usefulness and the limitations of the pricing model by using convertible traded on the Tel-Aviv stock exchange.